Use newton method to iterate infinitely to find an approximate solution to any equation.
Project description
NewtonMathSolver
使用牛顿法无限迭代求任意方程近似解
基础调用
from NewtonMathSolver import Tolerance, NewtonMathSolver
n = NewtonMathSolver('x - 1 = 10', 'x', 2, Tolerance(level=6))
print(n.iterate(10))
print(n.result)
与之等效的是
from NewtonMathSolver import Tolerance, NewtonMathSolver
n = NewtonMathSolver('x - 1 = 10', 'x', 2, 1e-6)
print(n.iterate(10))
print(n.result)
进一步探究
这样可以看到计算步骤
from NewtonMathSolver import Tolerance, NewtonMathSolver
n = NewtonMathSolver('x - 1 = 10', 'x', 2, Tolerance(level=6))
while 1 + 1 == 2:
n.iterate()
print(n.result)
if n.result.result:
break
容忍与误差
使用牛顿法通常会有误差,于是我们会将误差与设定的容忍度进行对比,容忍度即误差允许的最大值
这样可以设定一个可操作的误差
from NewtonMathSolver import Tolerance
t = Tolerance(1e-6)
与之等价的是
from NewtonMathSolver import Tolerance
t = Tolerance(level=6)
以及
from NewtonMathSolver import Tolerance
t = Tolerance(1e-6, 666)
# 若是同时存在两个参数,则tolerance优先
其可以进行多种操作
自增
from NewtonMathSolver import Tolerance
t = Tolerance(level=6)
以下操作均允许
t + 1
print('t + 1', t)
t + 1 1.000001
t - 1
print('t - 1', t)
t - 1 9.999999999177334e-07
t * 2
print('t * 2', t)
t * 2 1.9999999998354667e-06
t / 2
print('t / 2', t)
t / 2 9.999999999177334e-07
t ** 2
print('t ** 2', t)
t ** 2 9.999999998354668e-13
t ** (1 / 2)
print('t ** (1 / 2)', t)
t ** (1 / 2) 9.999999999177334e-07
t.more()
print('more', t)
more 9.999999999177333e-08
t.less()
print('less', t)
less 9.999999999177334e-07
逻辑运算
print(t == 0)
print(t > 0)
print(t >= 0)
print(t < 1)
print(t <= 1e-7)
False
True
True
True
False
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